- We add the parts of the ratio to find the total number of parts.
- There are 2 + 3 = 5 parts in the ratio in total.
- To find the value of one part we divide the total amount by the total number of parts.
- 50 ÷ 5 = 10.
- We multiply the ratio by the value of each part.
- 2:3 multiplied by 10 gives us 20:30.
- The 50 counters are shared into 20 counters to 30 counters.

**Find the value of one part of the ratio by dividing the amount by the total number of parts.**

**Multiply the ratio by the value of one part.**

- 2 + 3 = 5 and so there are 5 parts in the ratio in total.
- We divide by this total number of parts to find the value of each part.
- 50 ÷ 5 = 10.
- We multiply the original ratio by the value of each part.
- We have 20:30.

# How to Solve Ratio Problems

We are asked to share £50 in the ratio **2:3**.

This means that for every **two parts** a person receives, a second person is given **three parts**.

We begin by finding the **total number of parts**.

There are **two parts** highlighted in green and **three parts** highlighted in orange.

We have **five parts** in our ratio in total.

In total, **all five parts are worth £50**.

To be able to find out how much money each person is given, we need to know **how much one part is worth**.

Each part in the ratio must have the **same value**.

This means that £50 must be **shared equally** over the five parts.

To share equally, we **divide £50 by 5**.

50 ÷ 5 = 10

So, **each part is worth £10**.

Now that we know that **one part is worth £10**, we can find out **what two parts and three parts are worth**.

If one part is £10, **two parts** must equal £20.

£10 x 2 = **£20**

If one part is £10, **three parts** must equal £30.

£10 x 3 = **£30**

The money in this ratio problem has been shared **£20:£30**.

One person receives £20 and the other receives £30. We can check our answer by adding the two amounts to see if they make our original total.

£20 + £30 = £50

Now try our lesson on *How to Calculate a Ratio of a Number* where we break down the process of sharing in a ratio into three steps.